In the 1990s, a few prescient souls discerned in the American public an unmet appetite for uplifting true stories, by which I don't mean news or reportage so much as neatly packaged transitional incidents from strangers' lives. The hokey Chicken Soup for the Soul was an unexpected bestseller in 1993 (there are currently more than 100 books within the brand, including Chicken Soup for the Chiropractic Soul, and it is now branching out into convenience food, presumably to be eaten while weeping over inspirational chiropractic feats).

Two years later, the radio show This American Life began its tenancy on NPR, featuring sharply crafted non-fiction stories, some domestic and some broader in range and scope. Among the latter was Mike Daisey's infamous account of the working conditions in Apple's Chinese factories. The controversy that ignited when this story was revealed to be partially fictionalised (largely in order to fit known facts into a first-person narrative) underscores the intensity with which a growing audience requires not just truth but also authenticity – that slippery word – valuing verifiable experience above all else.

Authentic personal experience is precisely what The Moth endeavours to supply. A night of live storytelling, it was established in a sitting room in New York City in 1997 by George Dawes Green. He wanted to replicate the magical summer evenings of his years in Georgia, when friends would settle on a back porch to whip up tales drawn from their own lives. The rules are simple: the stories must be true and they must be told without notes, straight from the mouth to the ear, a direct encounter between speaker and audience. To date, more than 10,000 stories have been presented by a cast of performers that range from celebrities to convicts, astronauts to addicts; it is fluttering into the Edinburgh book festival next week.

Like a poetry slam, The Moth is a high-wire act, in which the narrator's willingness to expose herself, to take risks or reveal emotion is directly linked to audience appreciation. As Neil Gaiman, a regular performer, explains in his introduction to this compendium of the 50 most striking stories so far: "Honesty matters. Vulnerability matters. Being open about who you were at a moment in time when you were in a difficult or impossible place matters more than anything."

So what happens when these living stories are consigned to the page? Is there a loss of voltage, a dulling of intensity, once the live element has been removed? And what sort of material has been enrapturing audiences for 17 years?

The last question is the easiest to assess. At their core, these are motivational stories, in which extraordinary individuals pass through a period of adversity, emerging with some kind of moral, some realisation about the shape or direction of their lives. A boy with a paralysing stammer sees a jaguar in a cage at the Bronx Zoo. It ignites his love of animals, with whom he feels he can speak, and for whom he vows to provide a voice, assuming he can ever get a word out. Years later, he finds himself in the jungle in Belize, where he encounters wild jaguars and manages to make good his boyhood promise of protection.

An academic black girl from Indiana loses her scholarship and housing and ends up sleeping on outdoor furniture in her mother's garage. Determined to work her way back up, she takes a job as a home-healthcare aide, caring for a dying man who, to her horror, has a Klansman uniform hanging by his bed, not to mention a gloweringly hostile wife.

"I'd like to think," this latter story ends, "that I changed the way she thought about people of colour … And for myself, I got a job that gave me something to do every day, which I desperately needed. I had left Indiana to change the world. And I didn't; I couldn't. But I realised that even if I couldn't change the world, I could change a little piece of the world that I was in, and that was enough for me."

This could stand as a motto for almost all the stories here, though the littleness of the piece varies. Some of the narrators have made a considerable mark on the world. Dr George Lombardi recalls an incident from his early years as an expert in infectious diseases, in which he was summoned to India by a mysterious woman in order to save the life of Mother Teresa (a task that required battling an exquisitely suited emissary of the pope). The astronaut Michael Massimo provides a loping, self-deprecating account of trying to replace an instrument panel on the Hubble space telescope. Despite rehearsing the task for five whole years, an unexpected glitch plunged him into an abyss of loneliness, not helped by gazing down at his home planet, circling implacably hundreds of miles below.

These tales of exceptional achievement – winning the World Series, reporting from Afghanistan, competing in the Paralympics – are interleaved with another kind, in which people who have lost purchase on the world regain a sense of self-belief thanks to some unlikely concatenation of circumstance. An orderly in a hospital, utterly uninvolved in his own or anyone else's life, finds himself forced into action when he's trapped in an elevator with a dying man. A transgender woman, returning to her home town for her father's funeral, is greeted with unexpected sweetness by the football team in which she was once a quarterback.

Many of these stories are intensely moving. They're sentimental, which is to say they work on an emotional rather than an intellectual plane, engendering a non-specific desire to do better, to stand up straighter, to be kinder to strangers. In fact, they feel like sermons from some post-religious church, concrete manifestation of the message that people are good or that life is short.

It's a tone that infects even the many professional writers here, among them Adam Gopnik, Nathan Englander, Joyce Maynard and Malcolm Gladwell. Andrew Solomon, author of The Noonday Demon and Far From the Tree, recounts an experience in Senegal in which his blinding depression was treated by a ndeup, a local healer. The ritual involved climbing into a tiny makeshift wedding bed in the village square with a live ram. "I had been told," Solomon reports drily, "that it was very, very bad luck if the ram escaped", and so he clutches it to his bosom, as the ndeup wraps them in layers of blankets, before slitting its throat and drenching him in blood. It's an entertaining episode, complete with the requisite ringing moral about how badly western doctors treat depression.

After a while, this need to force every experience into the same trajectory begins to annoy. No doubt it's partially a consequence of the transition from speech. On stage, the audience can perceive signs of ambiguity or struggle that are invisible on the page. Physical presentation can amplify or contradict what is being said, undercutting sententiousness and adding depth. Performance also offers a visceral sense of value, both because the experience is live and as such unrepeatable and because one can gauge what delivery costs the speaker. Some of this can also be achieved through the written word, but it requires a different approach: more understated, more slippery, less direct.

Three of the stories here are about prison, two of them cheerfully hard-boiled. The third is by Damien Echols, of the West Memphis Three, who was on death row for over a decade and who gives a gruelling account of systematic spirit-breaking, of violence and humiliation. For years, he was imprisoned in a tiny cell in which the previous incumbent had drawn a very faint pencil shadow of himself on the wall before being taken off and executed. This is a writerly detail, the kind that lingers, that impresses itself on the imagination, more subtle and yet more tenacious than any crafted moral.

But the story I'll remember longest barely features the speaker at all, suggesting that "I" isn't the only empathy-generating machine. The novelist Richard Price reports as a bystander, observing a scene that played out in front of him, a conflict between a black man, a white boy and two officers from the NYPD. It's a model of journalistic reticence and restraint, an act of bearing witness to the lives of others. There's no sentimental coda, instead, it's just a piece of the world, passed on without comment, a welcome reminder of the lasting virtues of impersonal reportage.

• Olivia Laing's The Trip to Echo Spring is shortlisted for this year's Gordon Burn prize. To order The Mothfor £10.39 with free UK p&p call Guardian book service on 0330 333 6846 or go to guardianbookshop.co.uk. The Moth is at the Edinburgh international book festival on 23 August. edbookfest.co.uk.